Mathematical models for swimming in a viscoelastic fluid

在粘弹性流体中游泳的数学模型

• 批准号: 0615919
• 负责人: Thomas Powers
• 金额: --
• 依托单位: Brown University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-09-01 至 2009-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0615919&HistoricalAwards=false
• 关键词: Mathematical; models; swimming; viscoelastic; fluid

In this project, we will develop new mathematical models for swimming in a viscoelastic fluid. The project consists of three parts. The first is to combine a model for the sliding filaments of a sperm flagellum with resistive-force theory in the Maxwell model for a linearly viscoelastic fluid, and then to determine the swimming speed. This simple model will capture many of the features which will be present in more complicated but realistic models, and illuminate the fundamental principles of swimming in a viscoelastic fluid. The aim of the second part is to derive the slender-body equations for the forces acting on thin rods in a viscoelastic medium, analogous to the slender-body equations familiar from Stokes flow. Finally, the aim of the third part is to apply these models to the case of sperm swimming in mucus. For example, at a certain point during fertilization, sperm cells change their beat pattern to the asymmetric whip-like "hyperactivated" state. We will study how hyperactivity affects motility in the viscoelastic environments of the uterus and oviduct.This project is motivated by the fact that many swimming microorganisms encounter biological fluids with solid-like (elastic) properties as well as liquid-like (viscous) properties. Examples range from mammalian sperm in cervical fluid to the ulcer-causing bacterium Helicobacter pylori in the mucus layer lining the inside of the stomach. Despite the great importance of these examples for fertility and health, there have been few attempts to develop a quantitative theory for swimming in viscoelastic fluids; almost all previous efforts have focused on purely viscous fluids such as water. It is important to develop a theory for viscoelastic swimmers, since it will deepen our understanding of the physical constraints faced by mammalian sperm, leading to a better understanding of their biology and perhaps new clinical strategies for contraception or enhancing fertility for humans or livestock.

在这个项目中，我们将开发在粘弹性流体中游泳的新数学模型。 该项目由三部分组成。第一个是将精子鞭毛滑动细丝模型与线性粘弹性流体麦克斯韦模型中的阻力理论相结合，然后确定游动速度。 这个简单的模型将捕捉到更复杂但现实的模型中出现的许多特征，并阐明在粘弹性流体中游泳的基本原理。 第二部分的目的是推导作用在粘弹性介质中细杆上的力的细长体方程，类似于斯托克斯流中熟悉的细长体方程。 最后，第三部分的目的是将这些模型应用于精子在粘液中游动的情况。例如，在受精过程中的某个时刻，精子细胞将其节拍模式改变为不对称的鞭状“过度激活”状态。我们将研究多动症如何影响子宫和输卵管粘弹性环境中的运动性。该项目的动机是许多游动的微生物会遇到具有类固体（弹性）特性和类液体（粘性）特性的生物液体。 例子包括从宫颈液中的哺乳动物精子到胃内部粘液层中引起溃疡的幽门螺杆菌。尽管这些例子对于生育和健康非常重要，但很少有人尝试开发粘弹性流体中游泳的定量理论。几乎所有先前的努力都集中在纯粘性流体，例如水。发展粘弹性游泳者的理论非常重要，因为它将加深我们对哺乳动物精子所面临的物理限制的理解，从而更好地了解其生物学，并可能为避孕或提高人类或牲畜的生育能力提供新的临床策略。